document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72419>Question 72419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> during the early 1990's kelly invested 8000 into two different types of accounts within a bank certificates of deposit and savings account.  For her accounts she received 8% interest for her certificates of deposit and 6% for her savings account.  In total she earned 580 for the yeat.  How much money was invested in each type of account? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51861 by </B><A HREF=/tutors/aboutme.mpl?userid=bam878s><B>bam878s(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bam878s><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=51861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the portion invested into the CD account (certificate of deposit)<BR>\n" );
document.write( "Let y be the portion invested into the savings account.<BR>\n" );
document.write( "Now we already know that x + y = 8000, so let's solve this equation for y.\r<BR>\n" );
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document.write( "x + y = 8000 => y = 8000 - x.\r<BR>\n" );
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document.write( "Now we know x is invested at 8% and y is invested at 6%.  To find the amount each makes at the end of the year we take x(.08) + x.  Note x(.08) is the amount of interest that is made on that amount at the end of the year.  So we add x to this amount to get the total of x at the end of the year.  Similarly for y, we have y(.06) + y.\r<BR>\n" );
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document.write( "Now let's re-write these equations.\r<BR>\n" );
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document.write( "x(.08) + x = x(1.08), and<BR>\n" );
document.write( "y(.06) + y = y(1.06).\r<BR>\n" );
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document.write( "Now, since we know that 580 dollars was made on the TOTAL amount at the end of the year we know we end up with 8580.\r<BR>\n" );
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document.write( "Now we can write this:\r<BR>\n" );
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document.write( "x(1.08) + y(1.06) = 8580\r<BR>\n" );
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document.write( "Now, since we solved for y at the beginning, we can plug this value into this equation and solve for x.\r<BR>\n" );
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document.write( "x(1.08) + y(1.06) = 8580<BR>\n" );
document.write( "x(1.08) + (8000-x)(1.06) = 8580 (multiply 8000-x by 1.06)<BR>\n" );
document.write( "x(1.08) + 8480 - x(1.06) = 8580 (subtract 8480 from both sides)<BR>\n" );
document.write( "x(1.08) - x(1.06) = 100 (subtract x terms on the left hand side)<BR>\n" );
document.write( "x(.02) = 100 (divide both sides by .02)<BR>\n" );
document.write( "x = 5000.  \r<BR>\n" );
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document.write( "Now we can plug this value into the original equation to solve for y.\r<BR>\n" );
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document.write( "5000 + y = 8000<BR>\n" );
document.write( "y = 3000.\r<BR>\n" );
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document.write( "So, 5000 was invested into the CD and 3000 was invested into the savings account.\r<BR>\n" );
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document.write( "I hope this helps!! </SPAN>\n" );
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